Backward Stochastic Differential Equation on Hedging American Contingent Claims

We consider a general wealth process with a drift coefficient which is a function of the wealth process and the portfolio process with convex constraint. Existence and uniqueness of a minimal solution are established. We convert the problem of hedging American contingent claims into the problem of minimal solution of backward stochastic differential equation, and obtain the upper hedging price of American contingent claims. KeywordsAmerican Contingent Claim, Backward Stochastic Differential Equation